Method for detecting received signal sequences

ABSTRACT

This invention is a method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK (Multiple Phase Shift Keying) signal sequences. This invention uses previously received signal samples and previously decided data phases to generate a phase reference for the current operation of detecting the received signal sample. The phase reference can be easily generated by a recursive form.

BACKGROUND OF THE INVENTION

For an MPSK transmission system, differential detection is preferred over coherent detection if the phase coherence is hard to obtain. The conventional (one-symbol) differential detection method uses a delayed version of received signal sequence as a phase reference for detection, which is equivalent to using the previously received signal sample as the phase reference to detect the currently received signal sample. Such a phase reference is likely to have been corrupted by noise. Hence, the error performance of the conventional (one-symbol) differential detection method is somewhat worse than that of the coherent detection method. To improve the error performance of differential detection, several multiple-symbol differential detection methods have been proposed. Among them, the complexity of implementation for decision feedback differential phase detection (DF-DPD) is relatively low. The DF-DPD method is a simplified version of a method called decision feedback differential detection (DF-DD). By setting all the amplitudes of received signal samples to be constant, DF-DD reduces to DF-DPD. Either the DF-DD or the DF-DPD method employs L previously received signal samples and L-1 data phases which were previously decided to detect the currently received signal sample. The operation of DF-DD and DF-DPD can be briefly described as follows.

Suppose that differentially encoded MPSK signal sequences are transmitted over a communication channel. Let r(t) be the received signal for time t. Then, R(t')={r(t):-∞<t ≦t'} is the received signal sequence up to time t'. Let T be the time interval between two adjacent received signal samples. Through a certain process of the received signal sequence, we have the received signal sample for time kT which is ##EQU1## where P is the signal power, .O slashed._(k) is the modulation phase, θ_(k) is an arbitrary phase introduced by the channel, and N_(k) is a sample of noise. The modulation phase is .O slashed._(k) =2πm/M for some m ε{0,1, . . . , M-1}, where M is the number of points in the signal constellation which we use. Let x be an arbitrary phase value. We define x mod2π=x+2Kπ, where K is an integer such that -π<x+2Kπ≦π. The information data for time kT is carried by the data phase Δ.O slashed._(k) 32 (.O slashed._(k) -.O slashed._(k-1))mod 2π. There are M possible values of Δ.O slashed._(k) which correspond to the M possible information data. The received signal sample r_(k) can be expressed by

    r.sub.k 32 |r.sub.k |e.sup.jψ.sbsp.k,tm (2)

where |r_(k) | and ψ_(k) are the amplitude and phase of the received signal sample r_(k) respectively and j=√-1. The phase, ψ_(k), can be represented as

    ψ.sub.k 32 (.O slashed..sub.k +η.sub.k +θ.sub.k)mod2π,tm (3)

where η_(k) is the phase noise due to the existence of N_(k).

For the DF-DD method, the decision rule is to determine the data phase Δ.O slashed._(n) for time nT which is the one among all the M possible values of Δ.O slashed._(n) that maximizes ##EQU2## where Δψ_(n) (l)=ψ_(n-)ψ_(n-l) is the l-interval phase difference for time nT and Δ.O slashed._(n-i) is the data phase that has already been decided. for time (n-i)T. There are several ways to obtain Δψ_(n) (l). We may obtain Δψ_(n) (l) by subtracting ψ_(n-l), the phase of the received signal sample at time (n-l)T, from ψ_(n), the phase of the received signal sample at time nT. We may also obtain Δψ_(n) (l) by directly processing a received signal sequence and a delayed version of it to extract the phase difference. The parameter X_(n) can also be expressed as ##EQU3## which is a primitive phase reference for time (n-1)T and is derived from ψ_(n-1). Define ##EQU4## where K_(n-1).sup.(l) is an integer which is used such that -π<μ_(n).sup.(l) ≦π. The parameter μ_(n).sup.(l) is an estimated phase error of ψ_(n) obtained by comparing ψ_(n) with Ψ_(n-1).sup.(l) +Δ.O slashed._(n). Since the shape of the curve of cosx is similar to the shape of the curve of 1-x² for -π<x≦π, we can use an approximation to simplify the decision rule of DF-DD. The simplified decision rule is to find the one among M possible Δ.O slashed._(n) which minimizes ##EQU5##

Decision feedback differential phase detection (DF-DPD) is a simplified version of DF-DD, for which all the amplitude factors are considered as constant. That means the decision rule of DF-DPD is to determine Δ.O slashed._(n) which is the one among the M possible values of Δ.O slashed._(n) such that ##EQU6## is minimized. Either DF-DD or DF-DPD have pretty good error performance and relatively low complexity. However, there is still much room for improvement. For either DF-DD or DF-DPD, the current detection operation is dependent on L previously received signal sample and L-1 previously decided data phases. In general, increasing L will improve the error performance and will also increase the complexity of detection. In this invention, inventors propose a novel differential detection method, for which the current detection operation employs a phase reference which is dependent on all the previously received signal sample and all the previously decided data phases. The phase reference can be easily generated from a simple recursive form. The proposed defferential detection method has low complexity of detection and has very good error performance.

SUMMARY OF THE INVENTION

This invention is a method for detecting the received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences. This method uses previously received signal samples and previously decided data phases to generate a phase reference for the current operation of detecting the received signal sample. The phase reference can be easily generated by a recursive form. Therefore, the differential detection method of this invention has low complexity of detection. Moreover, the differential detection method of this invention has very good error performance.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates block diagram for the first embodiment;

FIG. 2 illustrates block diagram for the second embodiment;

FIG. 3 illustrates the simulation results of the the first embodiment for M=4 with various W, where DD represents the conventional differential detection and CD represents the coherent detection;

FIG. 4 illustrates the simulation results of the the first embodiment for M=8 with various W, where DD represents the conventional differential detection and CD represents the coherent detection;

FIG. 5 illustrates the simulation results of conventional DF-DPD for M=4 with various L, where DD represents the conventional differential detection and CD represents the coherent detection;

FIG. 6 illustrates the simnulation results of conventional DF-DPD for M=8, where DD represents the conventional differential detection and CD represents the coherent detection.

DESCRIPTION OF THE PREFERRED EMBODIMENT

This invention is a method for detecting the received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences. The output of the detection operation of the invention for time (n+1)T is denoted by Δ.O slashed._(n+1). In this invention, Δ.O slashed._(n+1) is chosen to be the one among the M possible values of Δ.O slashed._(n+1) such that ##EQU7## where

    Ω.sub.n+1 32 (Δφ.sub.n+1 -Δ.O slashed..sub.n+1) mod 2π,tm (11)

and Δφ_(n+1) is a parameter which is generated by a recursive form. This means that Δφ_(n+1) is a function of Δφ_(n), Δφ_(n-1), . . . , Δφ_(n-v), Δ.O slashed._(n), Δ.O slashed._(n-1), . . . , Δ.O slashed._(n-)μ and Δψ_(n+1) (1), where v and μ are nonnegative integers and Δψ_(n+1) (1) is the one-interval phase difference for time (n+1)T.

If the phase of the received signal sample for time (n+1)T, ψ_(n+1), is available, then Δφ_(n+1) can also be calculated by ψ_(n+1) -φ_(n), where the parameter φ_(n) is called the phase reference for time nT which is generated by a recursive form. This means that φ_(n) is a function of φ_(n-1), φ_(n-2), . . . , φ_(n-v-1), Δ.O slashed._(n), Δ.O slashed._(n-1), . . . , Δ.O slashed._(n-)μ and ψ_(n), where v and μ are nonnegative integers and ψ_(n) is the phase of a received signal sample for time nT.

The decision rule of finding a data phase Δ.O slashed._(n+1) such that -_(M).sup.π <Ω_(n+1) ≦_(m).sup.π is equivalent to finding a data phase Δ.O slashed._(n+1) that minimizes |Ω_(n+1) |.

Either the recursive form for generating Δφ_(n+1) or the recursive form for generating φ_(n) can be easily implemented and hence the differential detection method of this invention has low complexity of detection. Furthermore, the differential detection method of this invention has very good error performance.

We now show a specific recursive form which can easily generate the phase reference φ_(n) for time nT. The recursive form is given by ##EQU8## where W_(n) and W_(n) ^(') are weight factors assigned for n, and L_(n) is an integer which is used such that

    -π<(φ.sub.n-1 +Δ.O slashed..sub.n)-(ψ.sub.n +2L.sub.n π)≦π.tm (13)

The phase reference generated from the recursive form given in equation (12) is equivalent to the weighted sum of all the primitive phase references derived from previously received signal samples, i.e., ##EQU9## where I_(n).sup.(l) is an integer, a₀.sup.(1) and ##EQU10##

Hence, the proposed differential detection method takes into account the information from all the-previously received signal samples and all the previously decided data phases.

For the first embodiment, we use a sequence of phases of the received signal samples as input to generate a sequence of data phases as ouput. In the first embodiment, equation (12) is used with W_(n) =W and W_(n) ^(') =1 for all n. The block diagram for the first embodiment is shown in FIG. 1.

In some applications, the phases ψ_(n+1) and ψ_(n) may not be available while the one-interval phase difference for time (n+1)T, Δψ_(n+1) (1)=ψ_(n+1) -ψ_(n), is available. We will use a recursive form to generate Δψ_(n+1) directly. Note that the recursive form (12) is equivalent to the recursive form ##EQU11## where J_(n) is an interger which is used such that

    -π<Δφ.sub.n -Δ.O slashed..sub.n +2J.sub.n π≦π.tm (17)

The input of this detection operation is Δψ_(n+1) (1). The phase difference Δψ_(n+1) (1) can be obtained by subtracting ψ_(n) from ψ_(n+1) or by directly processing the received signal sequence and a delayed version of it so as to extract the phase difference.

For the second embodiment, we use a sequence of phase differences as input to generate a sequence of data phases as ouput. In the second embodiment, equation (16) is used with W_(n) =W and W_(n) ^(') =1 for all n. The block diagram for the second embodiment is shown in FIG. 2.

Error performance of the detection using the first embodiment over the additive white Gaussian noise (AWGN) channel for M=4 and 8 with various W, which are derived from simulation, are given in FIG. 3 and 4 respectively. For comparison, simulation results of the receiver using conventional DF-DPD over the AWGN channel for M=4 and 8 with various L are given in FIG. 5 and 6 respectively. Since the second embodiment is equivalent to the first embodiment, the error performance of the second embodiment is the same as that of the first embodiment. In all the simulations, we assume that θ_(k) is constant for all k.

For either conventional DF-DD or conventional DF-DPD, the error performance is better for larger L. However, a larger L implies a higher complexity of detection. For either the first embodiment or the second embodiment, the error performance is better for a larger W. Note that the complexity of detection using the proposed method is independent of W if we disregard the complexity of mathematical operations with large numbers. The choice of W will depend on the speed of the channel variation. In a fastly varying channel, small W is preferred.

In some applications, a more general recursive form for generating the phase reference will be used. The more general recursive form is ##EQU12## where W_(n).sup.(1), W_(n).sup.(2), W_(n).sup.(3) and W_(n).sup.(4) are weight factors assigned for n and L_(n).sup.(1) and L_(n).sup.(2) are integers which are used such that

    -π<(φ.sub.n-1 +Δ.O slashed..sub.n +2L.sub.n.sup.(1) π)-(ψ.sub.n +2L.sub.n.sup.(2) π)≦π.tm (19)

In some applications, the phase reference φ_(n) can be generated by several recursive equations. Let φ_(n) =φ_(n).sup.(1). The phase reference φ_(n).sup.(1) can be generated by recursive equations given by ##EQU13## for i ε{1,2. . . , q}, where W_(n).sup.(i,1), W_(n).sup.(i,2), . . . , W_(n).sup.(i,q+1), V_(n).sup.(i,1), V_(n).sup.(i,2), . . . , and V_(n).sup.(i,q+1) for i ε{1,2. . . , q} are weight factors assigned for n and L_(n).sup.(j) for j ε{1,2, . . . , q+1} is an integer which is used such that

    -π<(φ.sub.n-1.sup.(j) +Δ.O slashed..sub.n +2L.sub.n.sup.(j) π)-(ψ.sub.n +2L.sub.n.sup.(q+1) π)≦π.tm (21)

In some applications, the parameter Δφ_(n+1) can be generated by several recursive equations. Let Δφ_(n+1) =Δφ_(n+1).sup.(1), which is generated by recursive equations given by ##EQU14## for i ε{1,2. . . , q} where W_(n).sup.(i,1), W_(n).sup.(i,2), . . . , and W_(n).sup.(i,q+1) for i ε{1,2. . . , q} are weight factors assigned for n and J_(n).sup.(j) for j ε{1,2. . . , q} is an integer which is used such that

    -π<Δφ.sub.n.sup.(j) -Δ.O slashed..sub.n)+2J.sub.n.sup.(j) π≦π.tm (23)

In some applications, the phase reference φ₀ at the beginning time of operation (n=0) can be an arbitrarily assigned phase value to simplify the implementation. 

What is claimed is:
 1. A method for detecting received signal sequences of a communication system transmitting differentially encoded M P S K signal sequences, of which the output of an (n+1)th detection operation is ΔΦ_(n+1) that is chosen to be the one among M possible values of a data phase ΔΦ_(n+1) that minimizes |Ω_(n+1) | wherein

    Ω.sub.n+1 =(Δφ.sub.n+1 -ΔΦ.sub.n+1)mod 2π,(24)

whereby the parameter Δφ_(n+1) is a function of Δφ_(n), Δφ_(n-1), ΔΦ_(n), ΔΦ_(n-1), . . . , ΔΦ_(n-)μ and Δψ_(n+1) (1), wherein Δψ_(n+1) (1) is a one-interval phase difference for time (n+1)T v and μ are nonnegative integers, and wherein said Δφ_(n+1) is equal to Δφ_(n+1).sup.(1), which is generated by recursive equations given by ##EQU15## for i=ε{1,2. . . , q} whereby W_(n).sup.(i,1), W_(n).sup.(i,2), . . . and W_(n).sup.(i,q+1) for i=ε{1,2. . . , q} are weight factors assigned for n, an J_(n).sup.(i) for j=ε{1,2. . . , q}, is an integer which is used such that

    -π<(Δψ.sub.n.sup.(j) -ΔΦ.sub.n)+2J.sub.n.sup.(j) π≦π.                                         (26).


2. A method for detecting received signal sequences of a communication system transmitting differentially encoded M P S K signal sequences, wherein Δ100 _(n+1) is calculated by ψ_(n+1) -φ_(n), whereby the parameter φ_(n) is a phase reference that is a function of Δφ.sub.(n-1), Δ100 _(n-2), ΔΦ_(n-v-1), ΔφΦ_(n), ΔΦ_(n-1), . . . , ΔΦ_(n-)μ and ψ_(n) , wherein ψ_(n) is the phase of a received signal sample for time nT, wherein v and μ are nonnegative integers, and wherein said φ_(n) is equal to φ_(n).sup.(1), which is generated by recursive equations given by ##EQU16## for i=ε{1,2. . . , q} whereby W_(n).sup.(i,1), W_(n).sup.(i,2), . . . , W_(n).sup.(1,q+1), V_(n).sup.(1,1), V_(n).sup.(1,2), . . . , and V_(n).sup.(i,q+1) for i=ε{1,2. . . ,q} are weight factors assigned for n, an L_(n).sup.(j) for j=ε{1,2. . . , q+1},is an integer which is used such that

    -π<(Δφ.sub.n-1.sup.(j) +ΔΦ.sub.n +2L.sub.n.sup.(j) 90 )-(ψ.sub.n +2L.sub.n.sup.(q+1) π)≦π.tm (29).


3. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 2, wherein W_(n).sup.(i,j) =V_(n).sup.(i,j) for i ε{1,2, . . . , q} and j ε{1,2, . . . , q+1}.
 4. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 1, wherein Δφ_(n).sup.(i) is an arbitrarily assigned phase value instead of Δψ₁ for some i ε{1,2, . . . , q}.
 5. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 2, wherein φ₀.sup.(i) is an arbitrarily assigned phase value instead of ψ₀ for some i ε{1,2, . . . , q}.
 6. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 1, wherein q=1.
 7. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 2, wherein q=1.
 8. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 6, wherein W_(n).sup.(1,1) =W and W_(n).sup.(1,2) =W', whereby W and W' are constants.
 9. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 7, wherein W_(n).sup.(1,1) =V_(n).sup.(1,1) =W and W_(n).sup.(1,2) =W', whereby W and W' are constants.
 10. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 6, wherein W_(n).sup.(1,1) =W and W_(n).sup.(1,2) =W'|r_(n) |, whereby |r_(n) | is the amplitude of the n-th received signal sample, W and W' are constants.
 11. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 7, wherein W_(n).sup.(1,1) =V_(n).sup.(1,1) =W and W_(n).sup.(1,2) =V_(n).sup.(1,2) =W'|r_(n) |, whereby |r_(n) | is the amplitude of the n-th received signal sample, W and W' are constants.
 12. A method for detecting received signal sequences of a communication system transmitting differentially encoded MPSK signal sequences as in claim 7, wherein W_(n).sup.(1,1) =W₁, W_(n).sup.(1,2) =W₂ |r_(n) |, V_(n).sup.(1,1) =W₃, and V_(n).sup.(1,2) =W₄, whereby W₁, W₂, W₃, and W₄ are constants. 